I have never made reservations (not even sure if they still do that) and never have been turned away. US Park has capacity for probably something like 5,000 vehicles.
On spring break and holiday periods, they sometimes get fully booked (less likely in these tougher economic times). When that happens, US Park typically asks you to park in an aisle--they tell you which ones--and leave your keys, just as you would with valet parking. They will give you a special "valet parking" receipt and they will park your vehicle later, when a space is available.
When you arrive back in Detroit, just give the valet parking receipt to the driver, who will pick up your keys at the office and take you directly to your vehicle.
Re dropping off your bags first at check-in, I don't think there is a "one answer fits all". It pretty much depends upon the fitness levels of your party, how much luggage each person will be carrying and what you consider to be convenience.
If your airline offers curbside baggage check-in (call them or check their website to be sure), it wouldn't be a bad idea, though not really necessary either. I have done it with skis and golf clubs, for example, when traveling with several people. You just pull up, park curbside, unload, check-in and leave.
In fact, curbside check-in is the ONLY way that I would recommend going to the terminal first.
If curbside check-in is NOT available, you will have to pay for short-term parking near the terminal, lug your bags to the check-in counter, wait in line, then someone will have to do the round-trip to US Park. Please note that security regulations require ALL passengers to have government-issued photo ID and to check-in, in person.
I suppose that the driver could drop everyone off for counter-check in, then go on to US Park. That would be time-consuming for the driver and he/she still would have to take their luggage back to the terminal, check-in and go through security. Or 3 people hang out 20 minutes or longer with the driver's luggage.
Rather than a convenience, it may simply cost more, still require you to handle your luggage and also add 20 minutes or longer to the time you need to be at the airport.